The edge would need to be able to mount the network drive -- probably via CIFS (SMB/Samba) or NFS. Not sure what other methods are used with a NAS device.
There appears to be a CIFS module for Android described
HERE, but according to the post there it would require a custom ROM. (There are people posting in the Development section who have that problem beat.)
This other post says both NFS and CIFS are possible -- if you have your phone (aka eDGe) rooted.